Problem: Simplify the following expression: $q = \dfrac{-20t - 12}{-20t + 12}$ You can assume $t \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-20t - 12 = - (2\cdot2\cdot5 \cdot t) - (2\cdot2\cdot3)$ The denominator can be factored: $-20t + 12 = - (2\cdot2\cdot5 \cdot t) + (2\cdot2\cdot3)$ The greatest common factor of all the terms is $4$ Factoring out $4$ gives us: $q = \dfrac{(4)(-5t - 3)}{(4)(-5t + 3)}$ Dividing both the numerator and denominator by $4$ gives: $q = \dfrac{-5t - 3}{-5t + 3}$